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lesantik [10]
3 years ago
11

A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is

5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 8 students, he found the average time was 5.55 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.05 level of significance. Assume normality.
Mathematics
1 answer:
BabaBlast [244]3 years ago
7 0

Answer:

0.0384 < 0.05, which means that we can conclude that the mean amount of time that college students spend in the shower is significantly different from 5 minutes.

Step-by-step explanation:

A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes.

This means that the null hypothesis is H_{0} = 5

He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes.

This means that the alternate hypothesis is H_{a} \neq 5

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

Null hypothesis:

Tests H_{0} = 5, which means that \mu = 5

In a sample of 8 students, he found the average time was 5.55 minutes and the standard deviation was 0.75 minutes.

This means, respectively, that n = 8, \mu = 5.55, \sigma = 0.75

Test statistic:

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{5.55 - 5}{\frac{0.75}{\sqrt{8}}}

z = 2.07

Pvalue:

Since we are testing if the mean is different from a value, and z is positive. The pvalue is two multiplied by 1 subtracted by the pvalue of z = 2.07.

z = 2.07 has a pvalue of 0.9808

2*(1 - 0.9808) = 2*(0.0192) = 0.0384

Decision:

0.0384 < 0.05, which means that we can conclude that the mean amount of time that college students spend in the shower is significantly different from 5 minutes.

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lana66690 [7]

Answer:

  • h -102 = 331
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Step-by-step explanation:

Using the problem statement as the basis for the equation, we can write ...

  h -102 = 331

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Using the diagram as the basis for the equation, we could write it as ...

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The original height of the helicopter was 433 m.

3 0
2 years ago
Which of the following best defines an angle?
scoray [572]

Answer:

Third option

Step-by-step explanation:

The first definition is not as broad as it should be, therefore, while an angle does meet that criteria, it's not a general definition, hence, it is incorrect. The second one is incorrect as well because a parabola has a vertex, and it is certainly not an angle. This definition is not specific enough, so it will be eliminated. The last one is again, too specific. The third one is the best answer because it is broad enough while still being specific.

8 0
3 years ago
Pasta Place needs to make pasta with garlic cream sauce for 80 guests at a party. One batch of pasta calls for 3 cups of cream a
uysha [10]

Answer:

Total pints of cream will they need for the pasta = 7 pints

Step-by-step explanation:

Given - Pasta Place needs to make pasta with garlic cream sauce for 80 guests at a party. One batch of pasta calls for 3 cups of cream and feeds 10 people. The restaurant already has 5 pints of cream in the fridge.

To find - How many more pints of cream will they need for the pasta?

Solution -

10 people = 3 cups of cream

⇒80 people = 8×3 = 24 cups of cream

Now,

We know that,

1 cup = 0.5 pints

⇒24 cup = 24×0.5 = 12 pints.

Now,

Given that, The restaurant already has 5 pints of cream in the fridge.

So,

Total pints more needed = 12 - 5 = 7 pints.

∴ we get

Total pints of cream will they need for the pasta = 7 pints

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The area of a circle is 497 cm2. What is the circumference, in centimeters? Express
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Answer:

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Step-by-step explanation:

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April is an avid chess player. She sets up a coordinate system on her chess board so she can record the position of the pieces d
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Answer:

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Step-by-step explanation:

To solve this problem, we need to calculate the distance between two points in the XY coordinate plane.

The formula to calculate this distance is:

d = sqrt(dx^2 + dy^2)

where dx is the difference between the X coordinate of the points, dy is the difference between the Y coordinate of the points, and d is the distance.

(sqrt is the square root of what is in the parenthesis)

The first point (April's king) has X=4 and Y=2, the second point (the opponent's king) has X=7 and Y=8.

So, we have that dx = 4-7 = -3 and dy = 2-8 = -6

Now, we calculate the distance:

d = sqrt[ (-3)^2 + (-6)^2 ] = sqrt(9+36) = sqrt(45) = 6.7082 = 6.7

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